Rare-event sampling for stochastic dynamics in network systems using cluster updates

Abstract

Understanding the stochastic evolution in complex networks is a central challenge across physics, biology, engineering, social science, and finance. The most consequential macroscopic events, like cascading failures in communication networks, widespread epidemic outbreaks, and rapid shifts in societal opinions, often emerge from a confluence of rare, localized stochastic processes and need to pass certain bottlenecks. Standard forward-time simulation algorithms like the Gillespie method are inefficient for the investigation of such phenomena due to catastrophic rejection rates. Advanced rare-event techniques like splitting methods and transition-path sampling often suffer from kinetic trapping, path degeneracy, genealogical correlations, or critical slowing down when applied to complex heterogeneous networks. We propose to overcome this challenge by establishing a novel technique called conditional-path Monte Carlo (CPMC), inspired by loop algorithms from equilibrium condensed-matter physics. By employing non-local updates on spacetime clusters without rejections, CPMC generates a Markov chain of trajectories that all strictly respect the targeted macroscopic boundary conditions like the occurrence of a massive network failure. We demonstrate the framework's potential by performing a simple risk factor analysis for rare large-scale epidemic outbreaks in SIS dynamics on kinship networks.